LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dpoequ ( integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, integer INFO )

DPOEQU

Purpose:
``` DPOEQU computes row and column scalings intended to equilibrate a
symmetric positive definite matrix A and reduce its condition number
(with respect to the two-norm).  S contains the scale factors,
S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
choice of S puts the condition number of B within a factor N of the
smallest possible condition number over all possible diagonal
scalings.```
Parameters
 [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) The N-by-N symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] S ``` S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.``` [out] SCOND ``` SCOND is DOUBLE PRECISION If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.``` [out] AMAX ``` AMAX is DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the i-th diagonal element is nonpositive.```
Date
November 2011

Definition at line 114 of file dpoequ.f.

114 *
115 * -- LAPACK computational routine (version 3.4.0) --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 * November 2011
119 *
120 * .. Scalar Arguments ..
121  INTEGER info, lda, n
122  DOUBLE PRECISION amax, scond
123 * ..
124 * .. Array Arguments ..
125  DOUBLE PRECISION a( lda, * ), s( * )
126 * ..
127 *
128 * =====================================================================
129 *
130 * .. Parameters ..
131  DOUBLE PRECISION zero, one
132  parameter ( zero = 0.0d+0, one = 1.0d+0 )
133 * ..
134 * .. Local Scalars ..
135  INTEGER i
136  DOUBLE PRECISION smin
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL xerbla
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max, min, sqrt
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input parameters.
147 *
148  info = 0
149  IF( n.LT.0 ) THEN
150  info = -1
151  ELSE IF( lda.LT.max( 1, n ) ) THEN
152  info = -3
153  END IF
154  IF( info.NE.0 ) THEN
155  CALL xerbla( 'DPOEQU', -info )
156  RETURN
157  END IF
158 *
159 * Quick return if possible
160 *
161  IF( n.EQ.0 ) THEN
162  scond = one
163  amax = zero
164  RETURN
165  END IF
166 *
167 * Find the minimum and maximum diagonal elements.
168 *
169  s( 1 ) = a( 1, 1 )
170  smin = s( 1 )
171  amax = s( 1 )
172  DO 10 i = 2, n
173  s( i ) = a( i, i )
174  smin = min( smin, s( i ) )
175  amax = max( amax, s( i ) )
176  10 CONTINUE
177 *
178  IF( smin.LE.zero ) THEN
179 *
180 * Find the first non-positive diagonal element and return.
181 *
182  DO 20 i = 1, n
183  IF( s( i ).LE.zero ) THEN
184  info = i
185  RETURN
186  END IF
187  20 CONTINUE
188  ELSE
189 *
190 * Set the scale factors to the reciprocals
191 * of the diagonal elements.
192 *
193  DO 30 i = 1, n
194  s( i ) = one / sqrt( s( i ) )
195  30 CONTINUE
196 *
197 * Compute SCOND = min(S(I)) / max(S(I))
198 *
199  scond = sqrt( smin ) / sqrt( amax )
200  END IF
201  RETURN
202 *
203 * End of DPOEQU
204 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62

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